$J$ $K$ $L$ If: $ JL = 121$, $ JK = 9x + 8$, and $ KL = 9x + 5$, Find $KL$.
Explanation: From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {9x + 8} + {9x + 5} = {121}$ Combine like terms: $ 18x + 13 = {121}$ Subtract $13$ from both sides: $ 18x = 108$ Divide both sides by $18$ to find $x$ $ x = 6$ Substitute $6$ for $x$ in the expression that was given for $KL$ $ KL = 9({6}) + 5$ Simplify: $ {KL = 54 + 5}$ Simplify to find ${KL}$ : $ {KL = 59}$